Question

${2x}^{2} - 200 = 0$
${x}^{2} - 9 = 0$
${2x}^{2} - 50 = 0$
${2x}^{2} - 8 = 0$
${2x}^{2} + 5x = 0$
${ - 4x}^{2} + x = 0$
${6x}^{2} - 7 = 0$
${x}^{2} + 4x + 3 = 0$

${4x}^{2} - 12x = 0$
${x}^{2} - x + 1 = 0$
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Answer 1

Răspuns:

Explicație pas cu pas:

2x² - 200 = 0 <=> 2x² = 200 I:2  => x² = 100 => x₁,₂ = ±√100 = ±10

x²-9 = 0 => x² = 9 => x₁,₂ = ±√9 = ±3

2x²-50 = 0  => 2x² = 50 I:2  => x² = 25 => x₁,₂ = ±√25 => x₁,₂ = ±5

2x²-8 = 0 => 2x² = 8 I:2  => x² = 4  => x₁,₂ = ±√4 = x₁,₂ = ±2

2x²+5x = 0  <=> x(2x+5) = 0 => x₁ = 0 ; x₂ = -5/2

-4x²+x = 0 <=> x(-4x+1) = 0 => x₁=0 ; x₂ = 1/4

6x²-7 = 0  <=> 6x² = 7  => x² = 7/6 => x₁,₂ = ±√(7/6) = ±(√42)/6

x²+4x+3 = 0 <=> x²+3x+x+3 = 0 <=> x(x+3) + x+3 = 0 <=>

(x+3)(x+1) = 0 => x₁ = -3 ; x₂ = -1

4x²-12x = 0 <=> 4x(x-3) = 0 => x₁ = 0 ; x₂ = 3

x²-x+1 = 0  ; x₁,₂ ∉ R

a = 1 ; b = -1 ; c = 1

Δ = b²-4ac = (-1)²-4·1·1 = 1-4 = -3

√Δ = √(-3) = i√3

x₁,₂ = (-b±√Δ)/2a = (1±i√3)/2  ∈ C